Internal problem ID [3024]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 10
Problem number: 276.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-\sec \relax (y)-3 x \tan \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x) = sec(y(x))+3*x*tan(y(x)),y(x), singsol=all)
\[ y \relax (x ) = \arcsin \left (\frac {x^{4} c_{1}-1}{4 x}\right ) \]
✓ Solution by Mathematica
Time used: 9.352 (sec). Leaf size: 23
DSolve[x^2 y'[x]==Sec[y[x]]+3 x Tan[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ArcSin}\left (\frac {1}{4 x}+3 c_1 x^3\right ) \\ \end{align*}